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By employing retarded Green functions, the spin-wave spectrum and the layer-sublatticc magnetization in Heisenberg ferrimagnetic three-layer superlattices and three-layer systems are calculated within the framework of the linear spin-wave approximation. The effects of the interlayer exchange constants and the intralayer exchange constants on the magnetic properties of the two systems are compared with those for the corresponding three-sublattice bulk ferrimagnets. It is found that all the differences between the magnetic properties of these systems originate from the differences between the exchange couplings in the three dimensions of the systems. The quantum correlations, such as the competition, cancellation, and transmission of the effects of the exchange couplings, are important for the magnetic properties of the systems. The asymmetry of the systems plays an important role in the zero-point quantum fluctuations and, correspondingly, in the layer-sublattice magnetizations of the layers.

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